{"paper":{"title":"Homotopy Colimits of Algebras Over Cat-Operads and Iterated Loop Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Manfred Stelzer, Rainer M. Vogt, Zbigniew Fiedorowicz","submitted_at":"2011-09-01T19:15:49Z","abstract_excerpt":"We extend Thomason's homotopy colimit construction in the category of permutative categories to categories of algebras over an arbitrary $\\Cat$ operad and analyze its properties. We then use this homotopy colimit to prove that the classifying space functor induces an equivalence between the category of $n$-fold monoidal categories and the category of $\\mathcal{C}_n$-spaces after formally inverting certain classes of weak equivalences, where $\\mathcal{C}_n$ is the little $n$-cubes operad. As a consequence we obtain an equivalence of the categories of $n$-fold monoidal categories and the categor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0265","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}